# symmetric difference of the two sets

Let (X, M, u) be a finite measure space. Show that

a. if E, F, in M and u (the symmetric difference of E and F) = 0, then u(E) = u(F)

b. Say that E ~ F if u ( the symmetric difference of E and F) = 0; then ~ is an equivalence relation on M

c. For E, F in M, define rho (E, F) = u ( the symmetric difference of E and F). Then rho (E, G) is less or equal to rho (E, F) + rho (F, G), and hence rho defines a metric on the space M / ~ ( the difference of M and ~) of equivalence classes.

© BrainMass Inc. brainmass.com October 10, 2019, 3:33 am ad1c9bdddfhttps://brainmass.com/math/finite-element-method/symmetric-difference-of-the-two-sets-424933

#### Solution Summary

This solution denotes the symmetric difference of the two sets.

$2.19